Question

ax4 + bx2 + c=0 (a>0) (c>0)
The quadratic equation has two solutions If
1)b2>4ac
2) b2-4ac>0

Answer 1

The quadratic equation has two solutions if b^2 - 4ac > 0

Given the equation ax^4 + bx^2 + c=0

• Let P = x^2

Substitute into the formula to have:

• a(x^2)^2 + bx^2 + c =0

The equation becomes aP^2 + bP + c = 0

For us to have a unique solution, the discriminant b^2 - 4ac must be greater than zero. Hence the quadratic equation has two solutions if b^2 - 4ac > 0

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